Aromatic Red Cedar Or Eastern Red Cedar

Exterior soffit in texas

No that is not true. Curing or not curing has to do with the stain and what type of oils it has, not the wood. See this for more info: 

DECKSTAINHELP.COM "https://www.deckstainhelp.com/deck-stains/"

Types of Deck Stains in 2025 by Scott Paul: Pro Contractor

Learn about different types of deck stains: water-based, oil-based, solid, semi-solid, semi-transparent. Weigh pros and cons, find a deck stain that lasts!

As for new wood, you cannot stain it right away unless rough sawn: 

DECKSTAINHELP.COM "https://www.deckstainhelp.com/staining-a-new-deck/"

How to Stain a Brand New Deck: Best Way to Stain a New Deck

So you have a brand new deck and now it needs to be stained. We will teach you how to stain a new wood deck and how to prep a new deck for staining.

The aromatic cedar logs I am getting milled have been cut down for a couple months and the boards will be kiln dried after milling. What are the potential problems I could face if I do put only one coat of stain on this wood immediately using either wood rich timber oil or Armstrong Clark semi transparent? Will the stain try to peel or what? I’m in the commercial construction business and we never let wood “weather” prior to staining (usually ceilings, millwork, accent walls, all indoor). I know manufacturers say to wait but why?

And I know it won’t take the stain or penetrate as well not being weathered, but what issues could I have?

It will not penetrate correctly and could result in improper curing (sticky and tacky that will attract dirt, mold, etc) and potentially premature failure (peeling).

It will be at your own risk if you pre-stain but we never recommend it or do it for our restoration customers.